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Macroscopic Modelling of Vibration and Stability Problems in Prestressed Microperiodic Elastic Solids

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The aim of this contribution is to propose and apply a certain averaged (macroscopic) mathematical model for the analysis of vibration and stability problems of prestressed microperiodic elastic solids. In contrast to the known homogenized model [2], [3] the proposed model describes the effect of the period length on the macroscopic solid behaviour.

Formulation of the problemThe object of considerations is a description of dynamic behaviour of a microperiodic elastic composite solid subjected to initial stresses. This problem is not new.

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“…This problem is not new. We can mention here approaches based on the known equation of the elasticity theory, [1] or on the homogenized model equations [2], [3]. However, the first approach can be applied only to some special periodic structures (like laminates) and the second approach neglects the effect of the period length on the overall solid behaviour.…”

“…The aim of this contribution is to propose and apply a certain averaged (macroscopic) mathematical model for the analysis of vibration and stability problems of prestressed microperiodic elastic solids. In contrast to the known homogenized model [2], [3] the proposed model describes the effect of the period length on the macroscopic solid behaviour.…”

“…The 2D-model equations (2) describe plates with period length of an order of the plate thickness contrary to the known 2D-averaging procedures. In contrast to homogenized plate models also higher free vibration frequencies can be calculated from formulas (3). The effect of initial stresses on higher vibration frequency is small and can be neglected.…”